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Moderate

# Separation of Variables II

APCALC-0NUF3J

A function, $y(x)$, satisfies the equation $\cfrac{dy}{dx}=\cfrac{3x+2}{y}$ and passes through the point $(1, \, -4)$.

Find $y(x)$.

A

$y = \pm \sqrt {3{x^2} + 4x + 9}$

B

$y = \sqrt {3{x^2} + 4x + 9}$

C

$y = - \sqrt {3{x^2} + 4x + 9}$

D

$y = \pm \sqrt {3{x^2} + 4x} + 16-\sqrt{7}$